1.6.37 Fields, Groups, Rings

Condition: Let \( G \) be a cyclic group \( C_{n} \). Let \( a, b \in G \) and \( s \in \mathbb{N}, s \geq 1 \) such that \( a^{s}=b^{s} \), gcd \( (s, n)=1 \). Show that \( a=b \).